рус

System of Abstract System Principles

Vitaly Dubrovsky

ABSTRACT

The goal of this paper is to formulate system principles applicable to all systems. This paper is based on the assumption that the main purpose of the system approach is dealing with complexity, and the main method serving this purpose is analysis-synthesis. It employs methodological analysis that is based on (1) Kant's teaching that system is a concept of reason, applicable to sensible objects only indirectly through theoretical constructs; (2) the Activity Approach view that system ontology should incorporate system methods; and (3) the Aristotelian standard of formulating principles by means of opposition.

First, based on analysis of existing definitions of system, this paper identifies the principal system constituents as "unity," "parts," and "interrelationship" and main categorical oppositions as "complex-simple" and "external-internal." Second, the paper analyzes the earliest case of system analysis-synthesis--analysis of names in Plato's dialogue Cratylus--and identifies four stages of analysis-synthesis and four respective representations of system. Plato's method suggests a principal distinction between two types of "parts": (1) "units" that are of the same nature as unity and (2) "elements" that are of a different "simpler" nature. It also suggests a corresponding distinction between two types of "interrelationship": (1) "organization" as interrelationship of units and (2) "structure" as interrelationship of elements. Third, in terms of the categorical cross-opposition of Complex-Simple and External-Internal, the paper formulates four system principles of representation: Unity (external and complex), Units (external and simple), Elements (internal and simple), and Structure (internal and complex). The corresponding principles of method are Hierarchy, (external analysis-synthesis of unity in terms of units), Simple Reduction-Production (analysis-synthesis of externally simple units in terms of internally simple elements), Completeness (internal analysis-synthesis of a complete structure in terms of elements), and Complex Reduction-Production (analysis-synthesis of external complex Unity in terms of internal complex structure). Fourth, an ontological picture that incorporates all of the above system principles as a system of principles is constructed.

The paper concludes that the formulated principles are the abstract system principles and formulation of the concrete system principles would require unfolding of the abstract categorical cross-opposition into a concrete Aristotelian "attributive construct."

Keywords: system principles, cross-opposition, complex-simple, external-internal.

INTRODUCTION

Half a century ago Ludwig von Bertalanffy introduced a new discipline, General System Theory (GST). He defined the purpose of the new discipline as unification of science and its subject matter as formulation of general system principles, or principles applicable to all systems. Unfortunately, no such principles have been formulated yet. In the previous paper (Dubrovsky, 2001), I argued that the methods of GST are incapable of producing principles applicable to all systems, and that the limitations of the methods were caused by the use of a naturalistic ontology of system. The paper suggested an alternative methodology which is based on the assumption that the main purpose of the system approach is dealing with complexity, and the main method serving this purpose is analysis-synthesis. It is also based on (1) Kant's teaching that system is not a real object but a conception of reason; (2) the Activity Approach view that system ontology should incorporate system methods; and (3) the Aristotelian standard of formulating principles by means of opposition.

Following the methodology, this paper, in the first step, by analyzing existing definitions of system, identifies the principal system concepts and categorical oppositions. In the second step, the paper analyzes the earliest case of system analysis-synthesis, Plato's dialogue Cratylus, and identifies the principle stages of analysis-synthesis and corresponding system representations. In the third step, the paper reformulates these stages and representations in terms of the categorical oppositions, thus producing two respective types of system principles: "regulative" principles of method, and "constitutive" principles of representation. In the final step, the paper constructs an ontological picture that incorporates all these system principles as a system of principles.

PRINCIPAL SYSTEM CONSTITUENTS

AND MAIN CATEGORICAL OPPOSITIONS

Principal System Constituents: Unity, Parts, and Interrelationship

Definitions of system typically deal with complex wholes, simple parts, and interrelationship of the parts. Although Parts ("elements," "constituents," "components," etc.) and Interrelationship ("interactions," "structure," "arrangement," "organization," etc.) seem to be commonplace in dealing with complexity in science, the notion of the complex whole differs, not only between traditional reductionism and the system approach, but also among followers of the system approach themselves.

While traditional scientists believe that a complex whole is the sum of its parts (Russell, 1948), the system approach emphasizes Unity: "Systems, of course, have been studied for centuries, but something new has been added. … The tendency to study systems as an entity rather than as a conglomeration of parts…" (Ackoff, 1959).

In some cases, it is assumed that parts and their interrelationship automatically produce Unity. For example, for Ashby (1958) any conceivable set of variables constitutes a system and, therefore, is unity. At the same time, the system approach in general, and GST in particular, emphasize Unity ("consistent whole," "wholeness", "synergy", etc") as an ontological addition to parts and their interrelationship.

But even in the latter case, the view on Unity may differ. For example, in his Treatise on Systems, De Condillac (1749) gave historically the first definition of system, in which unity is achieved by a special arrangement of parts with one part--principle--uniting all other parts as a single basis for their explanation.

Every system is nothing else but an arrangement of different parts of some art or science in a certain order in which they mutually support each other and in which preceding parts explain the following ones. The parts which explain the other parts are called principles, and the fewer principles, the better the system, so the perfect system should have only one principle (de Condillac 1749/1938, p.3).

The most cited von Bertalanffy definition of system as "set of elements standing in interrelationship" (1968/1998, p.55; also p. 38) should not be taken in isolation from his explanation: "If we are speaking of 'systems', we mean 'wholes' or 'unities'" (p. 66). He characterized Unity as a complex that is "more than the sum of its parts", "new or emergent" entity, resulting from complete ("instant") composition of parts:

The meaning of the somewhat mystical expression, "the whole is more that the sum of its parts" is simply that constitutive characteristics are not explainable from the characteristics of the isolated parts. The characteristics of the complex, therefore, appear as "new" or "emergent"...We can also say: While we can conceive of a sum being composed gradually, a system as total of parts with its interrelations has to be conceived of as being composed instantly" (Von Bertalanffy 1969/1998, p.55).

But it was Immanuel Kant who emphasized the priority of unity over the parts and their interrelationship. According to Kant, unity is not something "new" or "emergent" from interrelationship of parts, but the opposite; it is unity that determines the parts and interrelationship:

By a system I mean the unity of various cognitions under one idea. This idea is the conception--given by reason--of the form of a whole, in so far as the conception determines a priori not only the limits of its content, but the place which each of its parts is to occupy. The scientific idea contains, therefore, the end, and the form of the whole which is in accordance with that end. The unity of the end, to which all the parts of the system relate, and through which all have a relation to each other, communicates unity to the whole system, so that the absence of any part can be immediately detected from our knowledge of the rest; and it determines a priori the limits of the system, thus excluding all contingent or arbitrary additions. The whole is thus an organism (articulatio), and not an aggregate (coacervatio); it may grow from within (per intussuscetionem), but it cannot increase by external additions (per oppositionem) (Kant 1787/1943, pp. 466-467).

Kant emphasized Unity as a separate entity, "a substantial whole" that can be thought "in isolation" from its parts:

When I speak of a whole, which necessarily consists of simple parts, I understand thereby only substantial whole, as the true composite; that is to say, I understand that contingent unity of the manifold which is given as perfectly isolated (at least in thought), placed in reciprocal connection, and thus constituted a unity (Kant 1781/1943, p. 248).

For Kant, Unity is also ontologically prior to parts and interrelationship, or "conjunction" (note that for Kant the ontological status of system is a conception of reason):

Conjunction is the representation of the synthetic unity of the manifold. This idea of unity, therefore, cannot arise out of that of conjunction; much rather does that idea, by combining itself with the representation of the manifold, render the conception of conjunction possible. (Kant 1787/1943, p.76).

 
 

Following Kant, I assume that system can be viewed as both a separate entity--Unity--and as parts in standing interrelationship "placed in reciprocal connection" by means of analysis-synthesis (Figure 1).

Figure 1. Relation between Unity and Conjunction (Parts and Interrelationship).

Categorical Oppositions of System: Form - Content, Complex-Simple, and External-Internal

The Opposition of Form-Content

Kant defines system as "the unity of various cognitions under one idea," or reasoning conception "of the form of a whole" that "determines a priori not only the limits of its content, but the place which each of its parts is to occupy". According to Kant, reason is itself "a system of investigation according to principles of unity, the material being supplied by experience alone" (Kant 1787/1943, p.414). Considering applicability of reason to experience only via media of theoretical constructs (Kant 1787/1943, p. 194), I conclude that the content that corresponds to system as a form is scientific conceptual constructs. In other words, system is a form that organizes its content--scientific concepts-- into unity.

 

The Opposition of Complex - Simple

We are accustomed to think of wholes as complex and parts as simple, so usage of the terms "complex whole" and "simple parts" is common and has a long tradition that can be traced at least down to Empedocles. Kant speaks "of a whole, which necessarily consists of simple parts" (Kant, p. 248) and for us it is a habit to "explain complex wholes in terms of simple parts." The identification of whole with complex and part with simple became a source of many paradoxes, because they belong to different levels of thought. The category of whole-parts belongs to the level that Kant calls "understanding," while complex-simple belongs to the level that Kant calls "reasoning", and there is no parallelism between the two.

In Aristotelian terms (Categories, Metaphysics), the opposition of whole-parts is of the "relative" type. Whole and parts are inseparable in thought, unthinkable without each other: when we say "whole" we mean that it consists of the corresponding parts; and when we say "part" we think of the whole of which it is a part. At the same time, the opposition of simple-complex is of the "possession-privation" type. Complex means privation of simplicity. We say that an object is simple because it is "easy to understand, deal with, use, etc." (Webster Dictionary). This can be thought of independently of any complexity. On the other hand "complex" always means lack of simplicity, which is traditionally associated with composite nature, and which calls for explanation by means of analyzing the complex into its simple constituents.

If we compose two right triangles (parts) into a square (whole), few people, if any, would interpret a square as something more complex than a triangle. At the same time, if we decompose a complex object into parts, they are not necessarily simple. For example, organs are not simple parts, if we try to understand how the organism works. Therefore, wholes are not necessarily complex and parts are not necessarily simple. However, wholes indeed can be complex and parts can be simple. Therefore, there is nothing wrong in the expression "complex whole" or "simple parts", if we understand that we are combining categorizations from two different levels of thought, understanding and reasoning, respectively. The purpose of decomposition is not always to obtain simple parts and the purpose of composition is not always to obtain a complex whole. At the same time, the purpose of analysis is always representation of complex entity in simple terms, and the purpose of synthesis is always representation of an entity as a complex unity. For these reasons, I conclude that representations of objects as systems should deal with complex wholes and simple parts, but the opposition relevant for representation of system itself, of course, on the level of reasoning, is "Complex - Simple" rather than "whole - part".

The Opposition of External - Internal

The opposition of external and internal is an important constituent of a typical definition of system. Applied to system, this opposition can have four different interpretations. The first and the most popular is a "spatial" interpretation, according to which all parts and their interrelationship are internal to the system. Because external-internal is a "relative" opposition, i.e. one cannot be thought of without the other, then if parts and interrelationship are inside system, then something should be outside of it. The latter is usually identified as the system's environment, a concept that is logically problematic (Dubrovsky, 2001).

The second interpretation of external-internal in relation to system is belonging or not belonging to the system: every entity that belongs to a system is considered internal, what does not belong to the system is external. According to Kant, a priori knowledge of limits of system content permits one to detect absence of any part and to exclude "any contingent or arbitrary additions". According to this meaning, the whole "may grow from within, but it cannot increase by external additions" (Kant 1787/1943, pp. 466-467). Based on this interpretation, I understand Kant's expression, "the place each of its [system's] parts is to occupy" as the place within the arrangement of the parts, not within the system. In the same way, I interpret von Bertalanffy's statement, "that the laws governing behavior of the parts can be stated only by considering the place of the parts in the whole" (von Bertalanffy 1968/1998, p. 67). This interpretation has nothing to do with "system environment."

The third "operational" interpretation of internal-external is a shift of position of a physical or symbolic entity into or out of the system. For example, von Bertalanffy's distinction between open and closed systems has this meaning of external-internal. Also, according to this interpretation, G. Shchedrovitsky (1975) identified the corresponding group of operations: insertion of an element into its place in the object's structure and reverse operation of extraction of an element out of the structure. I maintain that correct interpretation of the shift should not be spatial, i.e. exchange of material between system and its "environment," but as a shift of the entity's status from not being a part of a system to becoming its part and vice versa.

The fourth interpretation is external or internal view or perspective of a system analyst who can shift from external view to internal and vice versa. For example, an externally viewed system appears as Unity, while the internal view may reveal parts and their interrelationship. Note that such an interpretation also does not leave a place for "environment." For the reasons that will be clarified later, this paper favors this interpretation of external-internal.

Equipped with the categories of Complex-Simple and External-Internal and concepts of Unity, Parts, and Interrelationship, we will turn to the case study of the main method for dealing with complexity, the method of analysis-synthesis.

ANALYSIS-SYNTHESIS: THE CASE OF PLATO'S CRATYLUS

Introductory comments

System analysis-synthesis and Kant's levels of thought

From the beginning of the system thought, the procedure of analysis of complex wholes into simple parts and synthesis of the parts back into the whole were considered necessary for dealing with complexity. Also, from the very beginning, most thinkers perceived analysis and synthesis as inseparable "sides," "lines," or "phases" of the same method which is usually called "analysis":

You can understand a thing only if you can analyze it. If, for example, you wish to understand a machine, decompose it, carefully noting relations among all its parts; separate them, arrange them in such an order that would prevent any confusion. Then, if you re-assemble the parts, observing how they affect each other, you will see the composition of the entire machine and completely comprehend it. In this way you should treat all ideas, which are supposed to constitute some system (de Condillac, 1749/1938, p.178).

In this quotation, de Condillac describes the process of system analysis-synthesis applying the terms "decomposition" and "re-assembling" to material components of a machine. He then suggests applying the same method to "all ideas, which are supposed to constitute some system." Kant used the reasoning terms analysis and synthesis to describe this method. Kant's distinction among three levels of thought--perception, understanding, and reasoning--suggests the distinction among different concepts related to analysis-synthesis, which often are used synonymously. I suggest the following terminological use:

Level Of Thought

Method

Categories

Perception

Physical Disassembling-Assembling

Device - details, components

Understanding

Conceptual Decomposition-Composition

Whole - Parts

Reasoning

Categorical Analysis-Synthesis

Unity - units, elements

For example, we create a PC by assembling a motherboard, CPU, memory cards, keyboard, monitor, and other components, according to our understanding of composition of a computer with a processor, secondary storage, inputs, outputs, and data communication functional devices. But computer scientists used analytic-synthetic procedures to create the theoretical model of a computer as a complex system comprised of simple elements linked together to form the appropriate structure of a computer. It is important to distinguish among these three concepts because not every assembling of components results in what can be interpreted as a whole. The whole can be obtained only if assembling is controlled by the rules of conceptual decomposition-composition. Likewise, not every decomposition-composition results in obtaining simple parts or a complex whole, but only those which correspond to the principles of analysis-synthesis.

Our method is empirical study of classical cases of scientific analysis-synthesis that are usually described in terms of conceptual decomposition-composition and physical disassembling-assembling. This means that we must describe the stages of analysis-synthesis and corresponding representations using theoretical and empirical terms of a particular science first, and then reinterpret the stages and representations in the terms of the system concepts and categories.

Introductory notes to Plato's Cratylus

The earliest surviving example of system analysis-synthesis can be found in Plato's dialogue Cratylus (a general review of the dialogue can be found in A. E. Taylor, 1926). In the dialogue, Plato not only applies the method of analysis-synthesis to a particular object--name--, but, as he always does, reflexively formulates the main stages of the method. Plato starts with the problem of the origin of names: Do things have their names by nature, or they are they established arbitrarily by convention? Followers of Heraclitus and Parmenides defended the first view, while followers of Protagoras defended the second. The first theory does not explain, for example, how things could have different names in different languages. The second theory failed to explain how names could correctly indicate the things and be shared by everyone speaking the same language. To solve the problem, Plato assumed that names are instruments of human communication. To function effectively, they must correspond to the things they designate. Assuming that a good instrument is created by a "master" of instruments, and is used by a "master" of the appropriate activity, he suggests that a "master of words" creates names that communicate correct knowledge of things, so people can recognize them. Thus, names are not arbitrary, but, at the same time, they depend on the master who "legislates" the use of the names, or makes them standard, so people using the same language can understand each other. A master makes instruments under supervision of the master who uses them. In the case of words, "dialectician," a master who knows the essence of things, performs the supervision. In the dialogue, Socrates plays the role of such a dialectician. Using largely jocular etymology, Plato attempts to explain how a master of names could create "correct" complex names out of simple ones and the simple names out of sounds or letters.

Stage 1: Stepwise Decomposition-Composition of Complex Names in Terms of Simple Names

 

Plato starts his analysis-synthesis with the problem of how it is possible that names correctly indicate the nature of things they designate. He suggests that many names are compressed sentences or abbreviated phrases that include other names, and that their meaning is a compound of the meanings of the participating names (Plato, Cratylus, 421 b). Each such complex name is still a name, one word that designates one object. The correctness of such complex names can be established by decomposing them into their constituents and determining correctness of the latter. If the participating names are correct, then their initial composition is also correct. Since some of the constituents are themselves complex names, the procedure should be applied to them in turn. This stepwise decomposition-composition must stop at the level of primary names that are indivisible into other names (Plato, Cratylus, 421 e - 422 b). If primary names constituting a complex name are correct, then the complex name, as a correct compressed sentence, is correct (Plato, Cratylus, 422 c-d).

Stage 2: Decomposition-Composition of Primary Names in Terms of Sounds and Letters.

Decomposition of primary names into sounds or letters

The correctness of complex names could be established by means of their decomposition into primary names. But correctness of primary names cannot be established this way, because they are indivisible into simpler names. So to establish correctness of primary names one needs a new method (Plato, Cratylus, 422 b-e).

Comparing vocal language with gestures, Plato suggests that "a name is a vocal imitation of that which the vocal imitator names or imitates" (Plato, Cratylus, 423 b). Therefore, a master of names grasps the nature of things "in letters and syllables in such a manner as to imitate their essence" (Plato, Cratylus, 424 b). On this basis, Plato suggests a method for dealing with primary names. First, unlike stepwise decomposition of complex names into simpler ones until primary names are reached, Plato suggests decomposing primary names directly into separate sounds or letters, without decomposing them first into fragments, e.g., syllables:

But how shall we further analyze them, and where does the imitator begin? Imitation of the essence is made by syllables and letters. Ought we not, therefore, first to separate the letters, just as those who are beginning rhythm first distinguish the powers of elementary and then of compound sounds, and when they have done so, but not before, proceed to the consideration of rhythms?" (Plato, Cratylus, 424 c).

Establishing imitating correspondence between sounds and essences

Second, Plato suggests the method of finding how sounds or letters imitate essences by empirical discovery of which sound imitates which essence. He suggests creating two taxonomies, classes of sounds and letters "according to the knowledge of language" on one hand, and classes of primary-named things, according to their essences, on the other hand. He assumes that the classes are in mutual correspondence, so the correspondence between a particular group of sounds or letters and a certain essence can be established (Plato, Cratylus, 425d).

For example, by grouping the words that contain letter "r", Plato finds that "r" imitates motion (like in crush, trembling, bruise, and break) because a legislator of names observed that "the tongue was most agitated and least at rest in the pronunciation of this letter" (Plato, Cratylus, 426 d-e). The "equivalent" sound "s", belonging to the same class, also can imitate motion (Plato, Cratylus, 434 d). This explains why the same things can have different names in various languages. The legislator also "observed the liquid movement of "l", in the pronunciation of which the tongue slips, and in this he found the expression of smoothness" (like in "level" or "slip").

Assembling (re-assembling) primary names out of sounds or letters

Third, if correspondence of sounds or letters and essences they imitate were established correctly, then a master of names could assemble them into syllables and further into primary names that indicate things correctly by means of correct imitation of the essential features of things by participating sounds or letters:

And so, too, we shall apply letters to the expression of objects, either single letters when required, or several letters, and so we shall form syllables, as they are called, and from syllables make nouns and verbs, and thus, at last from the combinations of nouns and verbs arrive at language, large and fair and whole (Plato, Cratylus, 425a).

Stage 3: Decomposition-Composition of Complex Names, Sentences, and the Entire Language into/out-of Sounds

In the above quotation Plato suggests that after primary names ("nouns" and "verbs") are reconstructed in the material of sounds or letters, "from the combination of nouns and verbs" complex names and sentences as well as "language, large and fair and whole" should "at last" be reconstructed. This reconstruction is different from reconstruction of complex names from primary ones. In this case, Plato considers reconstruction of the entire language from sounds and letters imitating essences of the world. He explains: "Thus did the legislator, reducing all things into letters and syllables, and impressing on them names and signs, and out of them by imitation compounding other signs" (Plato, 427 d). Explaining "imitation," Plato warns that names are not duplicates of the things they name, but represent them as their audible portraits (430a-433b), so knowing the names does not mean knowing the things, it means recognizing the things by their essential features imitated by sounds and letters.

Plato did not and, obviously, could not, implement his program that was based on the fantastic theory that names indicate things by means of imitating the essential attributes of the things by sounds or letters. Nevertheless, the stages of analysis-synthesis that are formulated in Cratylus suggest very important distinctions and additions to the concepts of Unity, Parts, and Interrelationships.

FORMULATION OF PLATO'S STAGES IN THE SYSTEM TERMS

Units versus Elements

It is obvious from the above description of Plato's method that he uses two types of parts. In the first stage of Stepwise Decomposition-Composition of Complex Names in Terms of Simple Names, Plato calls parts of complex names "elements" even if they are complex names themselves. He calls simple names "primary elements". It is also important that he decomposes names into simpler names, or entities of the same essence, or nature, as the whole:

I think that you will acknowledge with me that one principle is applicable to all names, primary as well as secondary--when they are regarded simply as names, there is no difference in them. … All the names that we have been explaining were intended to indicate the nature of things. … And that this is true of the primary quite as much as of the secondary names is implied in their being names (Plato, Cratylus, 422 c-d).

At the second stage of Decomposition-Composition of Primary Names in Terms of Sounds and Letters, the parts constituting primary names, sounds and letters, are of different essence, or nature, than names. They do not indicate the things as names do; they imitate essential attributes of the things.

Long ago Vygotsky (1930) suggested using the term Unit for the parts that have the same essence as the whole (e.g. molecules of water are still water). For the parts that have different nature from the whole (e.g. hydrogen and oxygen, resulting from electrolysis of water, are not water), he suggested using the term Element. This paper follows this terminological tradition. The distinction between units and elements plays an essential role in every developed scientific and engineering discipline. In the context of general system approach, the distinction between Units and Elements was addressed by Toda and Shuford (1965), Wilson and Wilson (1966), and Dubrovsky and Shchedrovitsky (1971).

Organization versus Structure

The distinction between Units and Elements suggests the distinction between corresponding interrelationships. Plato based the decomposition-composition of complex names into/out-of simpler ones on the theory that a complex name is a compressed sentence composed of simpler names. In other words, a sentence is an arrangement of simple names corresponding to a complex one or, in system terms, the arrangement of simple units corresponding to complex ones. Such a theory defines two types of relations among units. The first type is relations of coordination, between units, e.g., grammatical agreement between words in number (singular or plural). The second is the hierarchical relation of "complex-simple," with complex Unity at the top and simple, or primary, Units at the bottom of the hierarchy. Together, relations of coordination and hierarchy define the interrelationship of Units.

Although Plato has not given a precise description of how sounds and letters should be combined into syllables, primary names, and further, he clearly distinguishes composition-decomposition of sounds or letters into larger constructs from decomposition-composition of complex names out of simple ones. For example, he decomposed complex words into simple ones in a stepwise manner; decomposing primary names, he jumped directly to the "material" elements, sounds or letters, omitting syllables. While the interrelationship of units can be defined in terms of organizational relations of coordination and hierarchy, the interrelationship of elements can be defined in terms of structural links, corresponding to operations of elementary decomposition-composition. Following G. Shchedrovitsky (1965), I will call interrelationship of Units Organization and interrelationship of elements Structure.

Besides interrelationship, e.g. arrangement and linkage, the terms "organization" and "structure" are used to denote an action of organizing and structuring and the results of such actions. When we speak about system representations, we mean the latter: Organization as a hierarchical composition of coordinated Units and Structure constituted by elements united by a network of links.

Reduction versus Production

Unlike the analysis of Unity into Units, or parts of the same essence as Unity (primary names are still names), analysis of primary Units into elements means loss of the essence (sounds or letters imitating essences are not words indicating things) and is usually characterized as reduction. Since analysis-synthesis is a single two-phase process, it requires that the analytic reduction phase should go hand-in-hand with the opposite synthetic production phase. The latter should start with the reproduction of simple units in terms of elements, continue through the hierarchy of Units, and, ultimately, reproduce Unity as Structure, i.e., in the terms of elements and links. What is meant here under "production", in the naturalistic mode usually is called emergence.

The case study of Plato's Cratylus resulted in principal distinctions between two types of system parts, Units and Elements, their respective relationships, Organization and Structure, and categorization of the respective stage of analysis-synthesis as Reduction-Production. Below, the paper reinterprets the identified in the case study stages of decomposition-composition and the appropriate representations in the terms of principal system concepts and categories.

OPPOSITION AND CROSS-OPPOSITION.

Aristotle has established the tradition of formulating principles by means of opposition. He also formulated the standard for opposition: principles must be opposed as two polar species upon the common basis of their genus (e.g. Physics, 191a4-5; Metaphysics, 1055a, 27-28; 1058a, 10). In some cases, formulation of principles requires more than one opposition. For example, to define "simple bodies", fire, air, water, and earth, Aristotle combines two oppositions of "hot-cold" and "dry-moist" into cross-opposition (Figure 2):

Hence, it is evident that the couplings of the elements will be four: hot with dry and moist with hot, and again cold with dry and cold with moist. And these four couples have attached themselves to the apparently simple bodies (Fire, Air, Water, and Earth) in a manner consonant with theory" (On Generation and Corruption, 330 a 33 - 330 b 2).

 

 

 Figure 2. Example of Aristotelian Cross-opposition

Cross-opposition is not a combination of two independent oppositions. Cross-opposites are interdependent because they share the same common basis. In case of simple bodies, the basis is "prime matter" that is defined by Aristotle as the substratum that underlies all transmutations of simple bodies one into another, while itself staying unchanged. Cross-opposites are also interdependent, because a member of one opposition does not exist without being coupled with a member of the other opposition. For example, hot does not exist without being dry or moist. Each couple constitutes form of a simple body. This form combined with the prime matter makes up the substance of a simple body (Aristotle, On Creation and Corruption).

ABSTRACT SYSTEM PRINCIPLES

 

Now we are ready to perform the main task of this paper: formulation of system principles. We will follow the Aristotelian standard of formulating principles by means of opposition. The above analysis of definitions of system yielded three categorical oppositions: form-content, complex-simple, and external-internal.

Figure 3. The Abstract Ontological Picture of System

Considering that system is the form of unifying reasoning upon theoretical content, we define "system form" by cross-opposition of "complex - simple" and "external - internal" upon the common basis of scientific knowledge as "system content". The cross-opposition of "complex-simple" and "external-internal" defines four system constituents and four relationships between each two of them (Figure 3). Since the definition is made by means of cross-opposition, the constituents and their relationships can be interpreted as system principles, principles of representation and principles of method, respectively.

System Principles of Representation

 

Principle of Unity: Complex object must be represented as external and complex

Representation of Unity (e.g., Plato's name) has two important characteristics: it must be external and complex. To deal with complexity of an object, it must be represented by its complex essence. The essence can be grasped from the external point of view by the object's essential manifestation, behavior, action, or property (e.g., "dialectician's" view of a name indicating an object). The complexity (not easy to explain or deal with) can be represented by a problem (e.g. by a problem of explaining how names can correctly indicate objects).

Principle of Units: Complex object must be represented as external and simple

In order to deal with complexity, the object must be represented by its simplest constituents still retaining its essence, simple units that still externally manifest the essence of an object (e.g. primary names indicating objects).

Principle of Elements: Complex object must be represented as internal and simple

Simple Units retaining the essence of Unity are still complex and, in turn, must be represented by their simple constituents. Since simple Units, by definition, cannot be decomposed into simpler units, the change of the analyst's view from external to internal is necessary. The internal point of view in relation to Units permits their further decomposition into Elements, the constituents that have a different essence from Unity, i.e. manifest different behavior, action, or property (e.g. sounds or letters that imitate essences). Elements cannot be decomposed further, so a way of explanation or dealing with the elements must be found in order to ultimately deal with the complex object.

Principle of Structure: Complex object must be represented as internal and complex

After simplicity (easiness of explanation or dealing with) is achieved with the elements, the complex object must be represented in simple terms. The elements must be combined into the Structure, an internal equivalent of Unity. Since Unity was defined as external and complex, the Structure can be equivalent to Unity only in its complexity as a combination of simple elements and links among them. It is assumed that structural representation provides an explanation of, or method for dealing with, the complex object.

System Principles of Method

Principle of Hierarchy: Stepwise analysis-synthesis of Unity in terms of hierarchy of Units

The first stage of the system analysis-synthesis of names, "stepwise decomposition-composition of complex names in terms of simple names", can be reformulated in the system terms as analysis-synthesis of Unity in terms of hierarchy of Units. This stage links two representations of a complex object Unity and Units (Figure 2) and can be characterized as external hierarchical analysis-synthesis. The stage defines a hierarchy of units, ordered according to their complexity, with Unity on the top and simple units on the bottom of the hierarchy.

Principle of Simple Reduction/Production: Analysis-synthesis of simple Units in terms of Elements

The second stage of the system analysis-synthesis of names, "decomposition-composition of primary names in terms of sounds and letters," can be reformulated in the system terms as analysis-synthesis of simple Units in terms of Elements. This stage links Units and Elements as representations of complex object (Figure 2). Since both simple Units and Elements are simple system representations, the stage can be characterized as simple analysis-synthesis. Since Units that have the same essence as Unity are analyzed into Elements that have different essence, and then the essence is restored back, the stage can be characterized as a simple reduction-production.

Principle of Completeness: Analysis-synthesis of complete Structure in terms of elements

The third stage of system analysis-synthesis of names, "decomposition-composition of complex names, sentences, and the entire language into/out-of sounds," can be reformulated in the system terms as analysis-synthesis of complete structure in terms of elements. This stage links Elements and Structure as representations of complex object (Figure 2). Although Plato has not formulated the requirement of completeness for Structure, the principle of completeness was formulated long ago by Kant and relatively recently by von Bertalanffy. Kant included the principle of completeness as an essential part of his definition of system, according to which, in relation to Unity, "the absence of any part can be immediately detected from our knowledge of the rest; and it determines a priori the limits of the system, thus excluding all contingent or arbitrary additions" (Kant 1787/1943, p. 467). Von Bertalanffy formulated the principle, explaining that only a complete structure corresponds to Unity: "While we can conceive of a sum being composed gradually, a system as total of parts with its interrelations has to be conceived of as being composed instantly" (Von Bertalanffy 1969/1998, p.55). Thus, completeness of Structure is a necessary requirement for the restoration of Unity "from within" in terms of Elements and links.

At the abstract level, the principle of completeness can be formulated in the following way: System's structure should include as its elements all entities necessary for, and exclude all entities preventing from, the effective reconstruction of Unity. A concrete formulation of this principle is the following: System's structure should include as its elements all entities without which, and exclude all entities with which, functioning of the system would be impossible or would degrade below certain tolerance level. Although this principle sounds very simple, it is too often violated in science and engineering.

Principle of Complex Reduction-Production: Analysis-synthesis of Unity in terms of Structure

In the Plato method there is no stage that links Unity and Structure (Figure 3): a peculiar stage of analysis-synthesis of complex Unity in terms of complex Structure. Such analysis-synthesis can be understood as mutual mapping of Unity and Structure. Mapping of Unity into Structure means its reduction to elements and links, or representation that loses its essence. The opposite mapping of Structure into Unity means restoration of Unity in terms of Structure, or production of Unity, when "the characteristics of the complex, therefore, appear as 'new' or 'emergent'" (Von Bertalanffy 1969/1998, p.55). Therefore, this stage can be characterized as complex reduction-production that requires internal-external shifts of the analyst's view and resolves the complexity of Unity as complexity. It is apparent that successful mutual mappings of Unity and Structure are impossible without three other stages. At the same time, the three stages are meaningless without this stage.

THE ONTOLOGICAL PICTURE OF SYSTEM:

 A SYSTEM OF SYSTEM PRINCIPLES

Systems Are Not Real but Actual

Figure 3 represents complex object in four different ways, each corresponding to a crossing of two stages of analysis-synthesis. A corresponding ontological picture has to combine all of the four representations and incorporate all four stages, or the entire method of analysis-synthesis. Traditionally, it is done by means of "configurator-model", a theoretical model that configures, or incorporates, different "sides" or properties, that are believed to belong to the same object (Lefebvre, 1962; Shchedrovitsky, 1984/1995). Lefebvre gives the following metaphorical example. Suppose one observer sees an object as a triangle while another sees it as a disc. They believe that both see the same object and combine their observations as a cone. As a configurator-model the cone "configures" triangle and disc as its projections. Thus, a configurator-model represents reality better than its projections and is usually used as an ontological picture. Currently existing configurator-models of system (e.g., Dubrovsky 2001) do not incorporate all representations and stages of analysis-synthesis, at least, because they do not distinguish between Units and Elements.

Another approach to ontological representations is called "configurator-plan" (Genisaretsky, 1966/1992; Shchedrovitsky, 1984/1995). A classical example of a configurator-plan is Bohr's complementarity principle that methodologically unites two mutually exclusive representations of light, particle and wave. Since all four system representations, Unit, Units, Elements, and Structure, are introduced by cross-opposition and, therefore, mutually exclusive, configurator-plan seems to be the way of building an ontological picture of system. In this case, eight principles depicted in Figure 3 constitute configurator-plan, or four representations connected by four stages of analysis-synthesis method, and thus can be considered the ontological picture of system.

As ontological picture, configurator-plan is not a naturalistic representation of a real object, or reality. It is a methodological representation of the actuality of analysis-synthesis with actual objects involved. While it is believed that reality and real objects are independent of our activities, actuality is our activity and actual objects are determined by our actions. In this view, reality and real objects are conceptual constructs resulting from reflexion upon our actions. Properties that actual objects, things, symbols, or concepts manifest depend on the actions they are involved in. At the same time, objects are usually included in more than one action and properties manifested in one action may be manifested independently of other actions involving the same object. The larger the number of actions in which an object is involved, the more independent the object's properties from each action, and the higher reality index it should be assigned.

As an actual object, in this paper, system is completely defined by the method of analysis-synthesis, so its index of reality is 0. At the same time, each of its four representations are involved in two stages of the method (Figure 3) and, therefore Unity, Units, Elements, and Structure, each of these representations, should be assigned a reality index of 1. Thus, the four representations of system are more real than completely actual system.

System is a System of Principles

According to Aristotle, a defining characteristic of reason is self-reflexion ("self-thinking thought") and, according to Kant, in self-reflexion, reason is itself a system (Kant, p. 414). As it was described above, in the non-reflexive interpretation, system is a set of principles imposed upon theoretical decomposition-composition and the corresponding design of theoretical models. In the reflexive interpretation, ontological picture of system (Figure 3) is itself a system. Its unity is represented by a method of dealing with complexity--analysis-synthesis. Its unit-principles, Unity, Units, Elements, and Structure are coordinated by respective principles of method. Each structural unit is composed of two non-opposite elements: Unity = External x Complex; Units = External x Simple; Elements = Internal x Simple; and Structure = Internal x Complex. Its Structure consists of the four elements linked by the cross-opposition: Complex, Simple, External, and Internal.

CONCLUSION

 

This paper has formulated system principles based on several assumptions. The first assumption was that the main purpose of the system approach is dealing with complexity by means of the method of analysis-synthesis. This paper demonstrates that a complex object or process is dealt with by means of four complementary concurrent representations coordinated by stages of analysis-synthesis. The "simplification" is achieved by complex reduction-production (of complex Unity in terms of simple Elements linked into complex Structure), mediated by simple reduction-production (of simple Units in terms of even simpler Elements).

The second assumption was based on Kant's view that system is not a real object, or thing, but a standard form for construction of theoretical models. The standard operates by means of system principles that organize procedures of decomposition-composition of theoretical models, and through them, procedures of physical disassembling-assembling of material objects or processes. Thus as a form, system can have only theoretical content, and is systematically applicable to real objects only through theoretical constructs. Sometimes system principles are applied, and sometimes successfully, to empirical material or practical problems directly, without explicit reference to theoretical models. In such cases, in fact, implicit ad hoc surrogate system theoretical models are used as the substitute. The surrogate system models can be successfully used only as a heuristic means and only if supplemented by practical expertise of the analysts.

The third assumption was the Activity Approach view that system ontology should incorporate system methods. This assumption led to the conclusion that systems are not real, but purely actual objects. In other words, real complex things or events are not systems, but can be studied or acted upon as systems according to system principles.

 

The fourth assumption was based on the Aristotelian standard of formulating principles by means of opposition. Since the above system principles were formulated by cross-opposition, I conclude that they are indeed principles, i.e. non-derived rules, laws, or trues from which other rules, laws, or trues can be derived. Since in their formulation, "no special hypotheses or statements were made about the nature of the system, of its elements or the relations between them" (von Bertalanffy 1969/1998, pp. 84-85), I conclude that they are indeed system principles applicable to all systems.

Contrary to the usual negative view of reduction by system theorists, this paper argues that reduction is a necessary stage of analysis-synthesis (of course in conjunction with production). Reduction-production not only permits us to deal with complexity in the simplest possible terms, but in the causal terms as well. Plato could say that names indicate things correctly because the sounds or letters they comprise correctly imitate the essential attributes of things and, being combined into names, produce indication of things.

This paper is focused on dealing only with complexity as a main purpose of the system approach. The General System Theory emphasizes another purpose--unity of science by means of interdisciplinarity. Since system principles are supposed to be applicable to all systems, this paper suggests than a non-disciplinary view of system can contribute to unification of science.

The cross opposition of complex-simple and external-internal permits formulation of only abstract system principles and can account only for the method of analysis-synthesis without taking into consideration other system methods. For example, such concrete system principles as Organization and Structure (as a network of links) were left out of the ontological picture of system and, therefore, out of the system of system principles. Also the ontological picture has not incorporated two other methods described by Shchedrovitsky (1975), system measurement and insertion-extraction of system elements. To accommodate these principles and methods, as well as to formulate other concrete system principles, we must develop the ontological picture beyond categorical opposition. The corresponding method of ontological construction, which I call "constructive attribution" (Dubrovsky, 1999), was first employed by Aristotle in Metaphysics. Constructive attribution could be used for development of concrete system ontology and formulation of concrete system principles. But this is a topic for another paper.

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